Numerical simulation of dense gas flows on unstructured grids with an implicit high resolution upwind Euler solver.

*(English)*Zbl 1060.76586Summary: The study of the dense gas flows which occur in many technological applications demands for fluid dynamic simulation tools incorporating complex thermodynamic models that are not usually available in commercial software. Moreover, the software mentioned can be used to study very interesting phenomena that usually go under the name of non-classical gasdynamics, which are theoretically predicted for high molecular weight fluids in the superheated region, close to saturation. This paper presents the numerical methods and models implemented in a computer code named zFlow which is capable of simulating inviscid dense gas flows in complex geometries. We give a detailed description of the space discretization method used to approximate the Euler equations on unstructured grids and for general equations of state, and also give a summary of the thermodynamic functions required by the mentioned formulation. The performance of the code is demonstrated by presenting two applications, the calculation of the transonic flow around an airfoil computed with both the ideal gas and a complex equation of state and the simulation of the non-classical phenomena occurring in a supersonic flow between two staggered sinusoidal blades. Non-classical effects are simulated in a supersonic flow of a siloxane using a Peng-Robinson-type equation of state. Siloxanes are a class of substances used as working fluids in organic Rankine cycles turbines.

##### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76M10 | Finite element methods applied to problems in fluid mechanics |

76N15 | Gas dynamics, general |